Robert B. Washburn

Bio: Robert B. Washburn is an academic researcher. The author has contributed to research in topics: Optimization problem & Lagrangian relaxation. The author has an hindex of 5, co-authored 7 publications receiving 325 citations.

A new relaxation algorithm and passive sensor data association

Abstract: The static problem of associating measurements at a given time from three angle-only sensors in the presence of clutter, missed detections, and an unknown number of targets is addressed. The measurement-target association problem is formulated as one of maximizing the joint likelihood function of the measurement partition. Mathematically, this formulation leads to a generalization of the 3-D assignment (matching) problem, which is known to be NP hard. The solution to the optimization problem developed is a Lagrangian relaxation technique that successively solves a series of generalized two-dimensional (2-D) assignment problems. The algorithm is illustrated by several application examples. >

Multiobject Tracking using Passive Sensors

Abstract: An architecture for a system to track multiple targets using passive sensors is examined in this paper. Attention is confined to the multitarget tracking capability at a single sensor. A practical algorithm has been designed within the framework of the optimal solution to the mathematical formulation of the multiobject tracking problem. The feasibility of utilizing the algorithm in practical scenarios is demonstrated with test results obtained using real data.

Assignment Algorithms for the Passive Sensor Data Association Problem

Abstract: This paper is concerned with the problem of associating measurements from multiple passive line-of-sight only sensors in the presence of clutter, missed detections and unknown number of targets The measurement-target association problem is formulated as one of maximizing the joint likelihood function of the measurement partition Mathematically, this formulation of the data association problem leads to a generalization of the multi-dimensional matching problem, which is known to be NP-complete ( of non polynomial complexity ) when the number of sensors S ≥ 3 Suboptimal algorithms are therefore of considerable importance In this paper we present two suboptimal algorithms - a backtracking algorithm with a complexity of order 0(M in M), where M is the number of possible measurement-target associations, and a relaxation algorithm that successively solves a series of generalized two-dimensional assignment problems, with the worst case complexity of 0(3k n3 ), where n is the number of reports from each sensor, and k is the number of relaxation iterations The performance of the backtracking algorithm is guaranteed to be much better than the "row-column" heuristic, which has complexity of 0(M) A nice feature of the relaxation approach is that the resulting primal and dual solutions provide a measure of how close the solution is to the (perhaps unknowable) optimal solution in terms of the duality gap For the passive sensor data association problem, the duality gaps are typically less than 1% We present comparisons between the two algorithms in terms of performance and time complexity in the context of passive sensor data-association problem involving three sensors Both of the algorithms are tested on a wide variety of scenarios involving a wide range of target densities, measurement accuracy, and false alarm and missed-detection probabilities

Performance Analysis for Hybrid State Estimation Problems

Abstract: Hybrid state estimation problems are statistical estimation problems in which both continuous-valued and discrete-valued states and parameters occur. The hybrid state model provides both a natural formulation for many types of surveillance and tracking problems and a powerful framework for deriving theoretically optimal and practical suboptimal tracking algorithms. This paper describes research in developing tools for evaluating the performance of optimal and suboptimal hybrid state estimation problems.

A Relaxation Algorithm for the Passive Sensor Data Association Problem

Abstract: This paper is concerned with the problem of associating measurements from multiple angle-only sensors in the presence of clutter, missed detections and unknown number of targets. The measurement-target association problem is formulated as one of maximizing the joint likelihood function of the measurement partition. Mathematically, this formulation of the data association problem leads to a generalization of the multi-dimensional matching (assignment) problem, which is known to be NP-complete when the number of sensors S ? 3, i.e., the complexity of an optimal algorithm increases exponentially with the size of the problem. The new solution to the optimization problem developed in this paper is a Lagrangian relaxation technique that successively solves a series of generalized two-dimensional assignment problems, with the worst case complexity of max [O(S n3), O(M)], where n is the number of reports from each sensor and M is the number of possible measurement-target associations. The dual optimization problem is solved via an accelerated subgradient method. A useful feature of the relaxation approach is that the resulting dual optimal cost is a lower bound on the feasible cost and, hence, provides a measure of how close the feasible solution is to the (perhaps unknowable) optimal solution. For the passive sensor data association problem, the feasible solution costs are typically within 1% of their corresponding dual optimal costs. The algorithm is illustrated via several examples.

The interacting multiple model algorithm for systems with Markovian switching coefficients

Abstract: An important problem in filtering for linear systems with Markovian switching coefficients (dynamic multiple model systems) is the management of hypotheses, which is necessary to limit the computational requirements. A novel approach to hypotheses merging is presented for this problem. The novelty lies in the timing of hypotheses merging. When applied to the problem of filtering for a linear system with Markovian coefficients, the method is an elegant way to derive the interacting-multiple-model (IMM) algorithm. Evaluation of the IMM algorithm shows that it performs well at a relatively low computational load. These results imply a significant change in the state of the art of approximate Bayesian filtering for systems with Markovian coefficients. >

Data fusion

Abstract: The development of the Internet in recent years has made it possible and useful to access many different information systems anywhere in the world to obtain information. While there is much research on the integration of heterogeneous information systems, most commercial systems stop short of the actual integration of available data. Data fusion is the process of fusing multiple records representing the same real-world object into a single, consistent, and clean representation.This article places data fusion into the greater context of data integration, precisely defines the goals of data fusion, namely, complete, concise, and consistent data, and highlights the challenges of data fusion, namely, uncertain and conflicting data values. We give an overview and classification of different ways of fusing data and present several techniques based on standard and advanced operators of the relational algebra and SQL. Finally, the article features a comprehensive survey of data integration systems from academia and industry, showing if and how data fusion is performed in each.

Interacting multiple model methods in target tracking: a survey

Abstract: The Interacting Multiple Model (IMM) estimator is a suboptimal hybrid filter that has been shown to be one of the most cost-effective hybrid state estimation schemes. The main feature of this algorithm is its ability to estimate the state of a dynamic system with several behavior modes which can "switch" from one to another. In particular, the IMM estimator can be a self-adjusting variable-bandwidth filter, which makes it natural for tracking maneuvering targets. The importance of this approach is that it is the best compromise available currently-between complexity and performance: its computational requirements are nearly linear in the size of the problem (number of models) while its performance is almost the same as that of an algorithm with quadratic complexity. The objective of this work is to survey and put in perspective the existing IMM methods for target tracking problems. Special attention is given to the assumptions underlying each algorithm and its applicability to various situations.